\newcommand{\grbf}[1] {\mbox{\boldmath${#1}$\unboldmath}}
\newcommand{\al}{\alpha}
\newcommand{\Eb}{E_{\beta}}
\newcommand{\Tc}{\textsf{T}}
\newcommand{\altt}{\frac{\alpha}{\theta}}
\newcommand{\beq} {\begin{equation}}
\newcommand{\eeq} {\end{equation}}
\newcommand{\bit}{\begin{itemize}}
\newcommand{\eit}{\end{itemize}}
\newcommand{\bde}{\begin{description}}
\newcommand{\ede}{\end{description}}
\newcommand{\bce}{\begin{center}}
\newcommand{\ece}{\end{center}}
\newcommand{\ben} {\begin{enumerate}}
\newcommand{\een} {\end{enumerate}}
\newcommand{\bea} {\begin{eqnarray}}
\newcommand{\eea} {\end{eqnarray}}
\newcommand{\barr} {\begin{array}}
\newcommand{\earr} {\end{array}}
\newcommand{\bean} {\begin{eqnarray*}}
\newcommand{\eean} {\end{eqnarray*}}
% Change
\def\totd{{\frac{d}{dt}}}
\def\domain{\int_{\Omega(t)}}
\def\bdrya{\int_{\gamma(\tau)}}
\newcommand{\pt}[1]{\frac{\partial #1}{\partial t}}
\newcommand{\iOm}[1]{\int_{\Omega(t)} #1 \, d\Omega}
\newcommand{\pn}[1]{\frac{\partial #1}{\partial n}}
\newcommand{\igt}[1]{\int_0^t\int_{\gamma(\tau)} #1 \,d\gamma dt}
\newcommand{\far}{\mathcal{F}}
\newcommand{\near}{\mathcal{N}}
%\renewcommand{\grbf}[1] {\mathbf{#1}}
\newcommand{\expt}[1] {e^{-n^2\pi^2({#1})}}
\newcommand{\gbf}[1] {\mathbf{#1}}
\newcommand{\dbl}{\mathcal{D}}
\newcommand{\sgl}{\mathcal{S}}
\newcommand{\splf}{\phi_{\tilde{\sgl}}}
\newcommand{\bdp}{\rho}
\newcommand{\TODO}[1]{ \fbox{\parbox{3in}{\bf #1}}}
\newcommand{\ts}{\triangle t}
\newcommand{\phit}{\tilde{\phi}}
\newcommand{\phib}{\breve{\phi}}
\newcommand{\bigO}{\mathcal{O}}
\newcommand{\sumn}{\sum_{n=1}^{p}}
\newcommand{\ifull}[1]{\int^{1}_{0} #1 \, d\theta}
\newcommand{\inear}[1]{\int^{10\alpha}_{0} #1 \, d\theta}
\newcommand{\ifar}[1]{\int_{10\alpha}^{1} #1 \, d\theta}
\newcommand{\ikers}[1]{\int_{0}^{1}\frac{1}{\theta^{\gamma}} #1 \, d\theta}
\newcommand{\ikerl}[1]{\int_{0}^{1}\log\theta #1 \, d\theta}
\newcommand{\kernel}{G_\delta (\norm{x_j - y_k}) }
\newcommand{\bdry}[1]{\int_{\gamma} #1 \, d\gamma}
\newcommand{\bol}[1]{\textbf{#1}}
\newcommand{\sint}{S_n}
%\newcommand{\sintt}{S_{\textbf{n}}}
\newcommand{\sintt}{S_{n_1 n_2}}
\newcommand{\dsintt}{\tilde{S}_{n_1 n_2}}
\newcommand{\cost}{C_n}
\newcommand{\DG}{\frac{\partial G}{\partial n}}
\newcommand{\tick}{\textbf{{\small $\hookrightarrow $ resolved}}}

%% used in codes
\newcommand{\cellc}{y_B}
\newcommand{\radc}{r_c}
\newcommand{\sd}{\sqrt{\delta}}
\newcommand{\momc}{I_C}
\newcommand{\radg}{r^g}
\newcommand{\gausst}{G_{\delta}}

%%%to be added to gbmacros
\newcommand{\fou}[1]{\hat{#1}_{\mathbf{n}}}
\newcommand{\vol}{\mathcal{V}}
\newcommand{\leaf}{L}
\newcommand{\mbf}{\mathbf{f}}
\newcommand{\mbx}{\mathbf{x}}
\newcommand{\mby}{\mathbf{y}}
\newcommand{\mbz}{\mathbf{z}}
\newcommand{\mbn}{\mathbf{n}}
\newcommand{\mci}{\mathcal{I}}
\newcommand{\mbk}{\mathbf{k}}
\newcommand{\mb}{\mathbf}
\newcommand{\mcb}{\mathcal{B}}
\newcommand{\mcc}{\mathcal{C}}
\newcommand{\ans}[1]{\emph{\textcolor{blue}{#1}}}
\newcommand{\norm}[1]{|\!| #1 |\!|}

\newcommand{\peq}{+\!\!=}
\newtheorem{prob}{Problem}[section]
\newtheorem{mydef}{Definition}[section]
 
